Arthur Eddington

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Eddington–Dirac number
Eddington–Finkelstein coordinates
Eddington stellar model
Eddington–Sweet circulation
AwardsRoyal Society Royal Medal (1928)
Smith's Prize (1907)
RAS Gold Medal (1924)
Henry Draper Medal (1924)
Bruce Medal (1924)
Knight Bachelor (1930)
Order of Merit (1938)
Scientific career
FieldsAstrophysics
InstitutionsTrinity College, Cambridge
Academic advisors
Doctoral students
Vibert Douglas

Sir Arthur Stanley Eddington

Eddington limit, the natural limit to the luminosity
of stars, or the radiation generated by accretion onto a compact object, is named in his honour.

Around 1920, he foreshadowed the discovery and mechanism of nuclear fusion processes in stars, in his paper "The Internal Constitution of the Stars".[3][4] At that time, the source of stellar energy was a complete mystery; Eddington was the first to correctly speculate that the source was fusion of hydrogen into helium.

Eddington wrote a number of articles that announced and explained Einstein's theory of general relativity to the English-speaking world. World War I had severed many lines of scientific communication, and new developments in German science were not well known in England. He also conducted an expedition to observe the solar eclipse of 29 May 1919 on the Island of Príncipe that provided one of the earliest confirmations of general relativity, and he became known for his popular expositions and interpretations of the theory.

Early years

Eddington was born 28 December 1882 in

Quaker parents, Arthur Henry Eddington, headmaster of the Quaker School, and Sarah Ann Shout.[5]

His father taught at a Quaker training college in

typhoid epidemic which swept England in 1884. His mother was left to bring up her two children with relatively little income. The family moved to Weston-super-Mare
where at first Stanley (as his mother and sister always called Eddington) was educated at home before spending three years at a preparatory school. The family lived at a house called Varzin, 42 Walliscote Road, Weston-super-Mare. A commemorative plaque on the building explains Sir Arthur's contribution to science.

In 1893 Eddington entered Brynmelyn School. He proved to be a most capable scholar, particularly in mathematics and English literature. His performance earned him a scholarship to Owens College, Manchester (what was later to become the University of Manchester), in 1898, which he was able to attend, having turned 16 that year. He spent the first year in a general course, but he turned to physics for the next three years. Eddington was greatly influenced by his physics and mathematics teachers, Arthur Schuster and Horace Lamb. At Manchester, Eddington lived at Dalton Hall, where he came under the lasting influence of the Quaker mathematician J. W. Graham. His progress was rapid, winning him several scholarships, and he graduated with a BSc in physics with First Class Honours in 1902.

Based on his performance at Owens College, he was awarded a scholarship to

Senior Wrangler. After receiving his M.A. in 1905, he began research on thermionic emission in the Cavendish Laboratory. This did not go well, and meanwhile he spent time teaching mathematics to first year engineering students. This hiatus was brief. Through a recommendation by E. T. Whittaker, his senior colleague at Trinity College, he secured a position at the Royal Observatory, Greenwich, where he was to embark on his career in astronomy, a career whose seeds had been sown even as a young child when he would often "try to count the stars".[6]

Plaque at 42 Walliscote Road, Weston-super-Mare
Eddington are on a horse; possibly during the Fifth Conference of the International Union for Co-operation in Solar Research, held in Bonn, Germany
Eddington, right, on a horse; possibly during the Fifth Conference of the International Union for Co-operation in Solar Research, held in Bonn, Germany, 1913

Astronomy

In January 1906, Eddington was nominated to the post of chief assistant to the

Bakerian Lecture in 1926.[7]

Eddington also investigated the interior of

Cepheid variable stars. He began by extending Karl Schwarzschild's earlier work on radiation pressure in Emden polytropic models. These models treated a star as a sphere of gas held up against gravity by internal thermal pressure, and one of Eddington's chief additions was to show that radiation pressure was necessary to prevent collapse of the sphere. He developed his model despite knowingly lacking firm foundations for understanding opacity and energy generation in the stellar interior. However, his results allowed for calculation of temperature, density and pressure at all points inside a star (thermodynamic anisotropy), and Eddington argued that his theory was so useful for further astrophysical investigation that it should be retained despite not being based on completely accepted physics. James Jeans contributed the important suggestion that stellar matter would certainly be ionized
, but that was the end of any collaboration between the pair, who became famous for their lively debates.

Eddington defended his method by pointing to the utility of his results, particularly his important

ideal gases. In the process of developing his stellar models, he sought to overturn current thinking about the sources of stellar energy. Jeans and others defended the Kelvin–Helmholtz mechanism
, which was based on classical mechanics, while Eddington speculated broadly about the qualitative and quantitative consequences of possible proton–electron annihilation and nuclear fusion processes.

Around 1920, he anticipated the discovery and mechanism of nuclear fusion processes in stars, in his paper "The Internal Constitution of the Stars".[3][4] At that time, the source of stellar energy was a complete mystery; Eddington correctly speculated that the source was fusion of hydrogen into helium, liberating enormous energy according to Einstein's equation E = mc2. This was a particularly remarkable development since at that time fusion and thermonuclear energy, and even the fact that stars are largely composed of hydrogen (see metallicity), had not yet been discovered. Eddington's paper, based on knowledge at the time, reasoned that:

  1. The leading theory of stellar energy, the contraction hypothesis (cf. the Kelvin–Helmholtz mechanism), should cause stars' rotation to visibly speed up due to
    Cepheid
    variable stars showed this was not happening.
  2. The only other known plausible source of energy was conversion of matter to energy; Einstein had shown some years earlier that a small amount of matter was equivalent to a large amount of energy.
  3. Francis Aston had also recently shown that the mass of a helium atom was about 0.8% less than the mass of the four hydrogen atoms which would, combined, form a helium atom, suggesting that if such a combination could happen, it would release considerable energy as a byproduct.
  4. If a star contained just 5% of fusible hydrogen, it would suffice to explain how stars got their energy. (We now know that most "ordinary" stars contain far more than 5% hydrogen.)
  5. Further elements might also be fused, and other scientists had speculated that stars were the "crucible" in which light elements combined to create heavy elements, but without more-accurate measurements of their atomic masses nothing more could be said at the time.

All of these speculations were proven correct in the following decades.

With these assumptions, he demonstrated that the interior temperature of stars must be millions of degrees. In 1924, he discovered the mass–luminosity relation for stars (see Lecchini in § Further reading). Despite some disagreement, Eddington's models were eventually accepted as a powerful tool for further investigation, particularly in issues of stellar evolution. The confirmation of his estimated stellar diameters by Michelson in 1920 proved crucial in convincing astronomers unused to Eddington's intuitive, exploratory style. Eddington's theory appeared in mature form in 1926 as The Internal Constitution of the Stars, which became an important text for training an entire generation of astrophysicists.

Eddington's work in

quantum physics, including the use of degeneracy physics
in describing dwarf stars.

Dispute with Chandrasekhar on the mass limit of stars

Main article: Chandrasekhar–Eddington dispute

The topic of extension of his models precipitated his dispute with Subrahmanyan Chandrasekhar, who was then a student at Cambridge. Chandrasekhar's work presaged the discovery of black holes, which at the time seemed so absurdly non-physical that Eddington refused to believe that Chandrasekhar's purely mathematical derivation had consequences for the real world. Eddington was wrong and his motivation is controversial. Chandrasekhar's narrative of this incident, in which his work is harshly rejected, portrays Eddington as rather cruel and dogmatic. Chandra benefited from his friendship with Eddington. It was Eddington and Milne who put up Chandra's name for the fellowship for the Royal Society which Chandra obtained. An FRS meant he was at the Cambridge high-table with all the luminaries and a very comfortable endowment for research. Eddington's criticism seems to have been based partly on a suspicion that a purely mathematical derivation from relativity theory was not enough to explain the seemingly daunting physical paradoxes that were inherent to degenerate stars, but to have "raised irrelevant objections" in addition, as Thanu Padmanabhan puts it.[8]

Relativity

During World War I, Eddington was secretary of the Royal Astronomical Society, which meant he was the first to receive a series of letters and papers from Willem de Sitter regarding Einstein's theory of general relativity. Eddington was fortunate in being not only one of the few astronomers with the mathematical skills to understand general relativity, but owing to his internationalist and pacifist views inspired by his Quaker religious beliefs,[6][9] one of the few at the time who was still interested in pursuing a theory developed by a German physicist. He quickly became the chief supporter and expositor of relativity in Britain. He and Astronomer Royal Frank Watson Dyson organized two expeditions to observe a solar eclipse in 1919 to make the first empirical test of Einstein's theory: the measurement of the deflection of light by the Sun's gravitational field. In fact, Dyson's argument for the indispensability of Eddington's expertise in this test was what prevented Eddington from eventually having to enter military service.[6][9]

When conscription was introduced in Britain on 2 March 1916, Eddington intended to apply for an exemption as a

Red Cross, or as a harvest labourer. However, the tribunal's decision to grant a further twelve months' exemption from military service was on condition of Eddington continuing his astronomy work, in particular in preparation for the Príncipe expedition.[6][9]
The war ended before the end of his exemption.

solar eclipse of 29 May 1919, presented in his 1920 paper announcing its success, confirming Einstein
's theory that light "bends"

After the war, Eddington travelled to the island of Príncipe off the west coast of Africa to watch the solar eclipse of 29 May 1919. During the eclipse, he took pictures of the stars (several stars in the Hyades cluster, including Kappa Tauri of the constellation Taurus) whose line of sight from the Earth happened to be near the Sun's location in the sky at that time of year.[10] This effect is noticeable only during a total solar eclipse when the sky is dark enough to see stars which are normally obscured by the Sun's brightness. According to the theory of general relativity, stars with light rays that passed near the Sun would appear to have been slightly shifted because their light had been curved by its gravitational field. Eddington showed that Newtonian gravitation could be interpreted to predict half the shift predicted by Einstein.

Eddington's observations published the next year[10] allegedly confirmed Einstein's theory, and were hailed at the time as evidence of general relativity over the Newtonian model. The news was reported in newspapers all over the world as a major story. Afterward, Eddington embarked on a campaign to popularize relativity and the expedition as landmarks both in scientific development and international scientific relations.[11]

It has been claimed that Eddington's observations were of poor quality, and he had unjustly discounted simultaneous observations at

Sobral, Brazil, which appeared closer to the Newtonian model, but a 1979 re-analysis with modern measuring equipment and contemporary software validated Eddington's results and conclusions.[12] The quality of the 1919 results was indeed poor compared to later observations, but was sufficient to persuade contemporary astronomers. The rejection of the results from the expedition to Brazil was due to a defect in the telescopes used which, again, was completely accepted and well understood by contemporary astronomers.[13]

The minute book of Cambridge ∇2V Club for the meeting where Eddington presented his observations of the curvature of light around the Sun, confirming Einstein's theory of general relativity. They include the line "A general discussion followed. The President remarked that the 83rd meeting was historic".

Throughout this period, Eddington lectured on relativity, and was particularly well known for his ability to explain the concepts in lay terms as well as scientific. He collected many of these into the Mathematical Theory of Relativity in 1923, which Albert Einstein suggested was "the finest presentation of the subject in any language." He was an early advocate of Einstein's general relativity, and an interesting anecdote well illustrates his humour and personal intellectual investment: Ludwik Silberstein, a physicist who thought of himself as an expert on relativity, approached Eddington at the Royal Society's (6 November) 1919 meeting where he had defended Einstein's relativity with his Brazil-Príncipe solar eclipse calculations with some degree of scepticism, and ruefully charged Arthur as one who claimed to be one of three men who actually understood the theory (Silberstein, of course, was including himself and Einstein as the other). When Eddington refrained from replying, he insisted Arthur not be "so shy", whereupon Eddington replied, "Oh, no! I was wondering who the third one might be!"[14]

Cosmology

Eddington was also heavily involved with the development of the first generation of general relativistic cosmological models. He had been investigating the instability of the Einstein universe when he learned of both Lemaître's 1927 paper postulating an expanding or contracting universe and Hubble's work on the recession of the spiral nebulae. He felt the cosmological constant must have played the crucial role in the universe's evolution from an Einsteinian steady state to its current expanding state, and most of his cosmological investigations focused on the constant's significance and characteristics. In The Mathematical Theory of Relativity, Eddington interpreted the cosmological constant to mean that the universe is "self-gauging".

Fundamental theory and the Eddington number

During the 1920s until his death, Eddington increasingly concentrated on what he called "

gravitation. At first he progressed along "traditional" lines, but turned increasingly to an almost numerological
analysis of the dimensionless ratios of fundamental constants.

His basic approach was to combine several fundamental constants in order to produce a dimensionless number. In many cases these would result in numbers close to 1040, its square, or its square root. He was convinced that the mass of the proton and the charge of the electron were a "natural and complete specification for constructing a Universe" and that their values were not accidental. One of the discoverers of quantum mechanics, Paul Dirac, also pursued this line of investigation, which has become known as the Dirac large numbers hypothesis.[15] A somewhat damaging statement in his defence of these concepts involved the fine-structure constant, α. At the time it was measured to be very close to 1/136, and he argued that the value should in fact be exactly 1/136 for epistemological reasons. Later measurements placed the value much closer to 1/137, at which point he switched his line of reasoning to argue that one more should be added to the degrees of freedom, so that the value should in fact be exactly 1/137, the Eddington number.[16] Wags at the time started calling him "Arthur Adding-one".[17] This change of stance detracted from Eddington's credibility in the physics community. The current CODATA value is 1/137.035999084(21).[18]

Eddington believed he had identified an algebraic basis for fundamental physics, which he termed "E-numbers" (representing a certain

grand unified theory. Moreover, Eddington's emphasis on the values of the fundamental constants, and specifically upon dimensionless numbers derived from them, is nowadays a central concern of physics. In particular, he predicted a number of hydrogen atoms in the Universe 136 × 2256 ≈ 1.57 1079, or equivalently the half of the total number of particles protons + electrons.[19]
He did not complete this line of research before his death in 1944; his book Fundamental Theory was published posthumously in 1948.

Eddington number for cycling

Eddington is credited with devising a measure of a cyclist's long-distance riding achievements. The Eddington number in the context of cycling is defined as the maximum number E such that the cyclist has cycled at least E miles on at least E days.[20][21]

For example, an Eddington number of 70 would imply that the cyclist has cycled at least 70 miles in a day on at least 70 occasions. Achieving a high Eddington number is difficult, since moving from, say, 70 to 75 will (probably) require more than five new long-distance rides, since any rides shorter than 75 miles will no longer be included in the reckoning. Eddington's own life-time E-number was 84.[22]

The Eddington number for cycling is analogous to the h-index that quantifies both the actual scientific productivity and the apparent scientific impact of a scientist.[20]

Philosophy

Idealism

Eddington wrote in his book The Nature of the Physical World that "The stuff of the world is mind-stuff."

The mind-stuff of the world is, of course, something more general than our individual conscious minds ... The mind-stuff is not spread in space and time; these are part of the cyclic scheme ultimately derived out of it ... It is necessary to keep reminding ourselves that all knowledge of our environment from which the world of physics is constructed, has entered in the form of messages transmitted along the nerves to the seat of consciousness ... Consciousness is not sharply defined, but fades into subconsciousness; and beyond that we must postulate something indefinite but yet continuous with our mental nature ... It is difficult for the matter-of-fact physicist to accept the view that the substratum of everything is of mental character. But no one can deny that mind is the first and most direct thing in our experience, and all else is remote inference.

— Eddington, The Nature of the Physical World, 276–81.

The

idealist
conclusion was not integral to his epistemology but was based on two main arguments.

The first derives directly from current physical theory. Briefly, mechanical theories of the ether and of the behaviour of fundamental particles have been discarded in both relativity and quantum physics. From this, Eddington inferred that a materialistic metaphysics was outmoded and that, in consequence, since the disjunction of materialism or idealism are assumed to be exhaustive, an idealistic metaphysics is required. The second, and more interesting argument, was based on Eddington's epistemology, and may be regarded as consisting of two parts. First, all we know of the objective world is its structure, and the structure of the objective world is precisely mirrored in our own consciousness. We therefore have no reason to doubt that the objective world too is "mind-stuff". Dualistic metaphysics, then, cannot be evidentially supported.

But, second, not only can we not know that the objective world is nonmentalistic, we also cannot intelligibly suppose that it could be material. To conceive of a dualism entails attributing material properties to the objective world. However, this presupposes that we could observe that the objective world has material properties. But this is absurd, for whatever is observed must ultimately be the content of our own consciousness, and consequently, nonmaterial.

Eddington believed that physics cannot explain consciousness - "light waves are propagated from the table to the eye; chemical changes occur in the retina; propagation of some kind occurs in the optic nerves; atomic changes follow in the brain. Just where the final leap into consciousness occurs is not clear. We do not know the last stage of the message in the physical world before it became a sensation in consciousness".[23]

philosophical idealism
"the thesis that reality is basically mental".

intelligibility of the world: that our minds and the physical world are made of the same "stuff" and that our minds are the inescapable connection to the world.[24]
As De Koninck quotes Eddington,

There is a doctrine well known to philosophers that the moon ceases to exist when no one is looking at it. I will not discuss the doctrine since I have not the least idea what is the meaning of the word existence when used in this connection. At any rate the science of astronomy has not been based on this spasmodic kind of moon. In the scientific world (which has to fulfill functions less vague than merely existing) there is a moon which appeared on the scene before the astronomer; it reflects sunlight when no one sees it; it has mass when no one is measuring the mass; it is distant 240,000 miles from the earth when no one is surveying the distance; and it will eclipse the sun in 1999 even if the human race has succeeded in killing itself off before that date.

— Eddington, The Nature of the Physical World, 226

Indeterminism

See also: Indeterminism and Indeterminism in science

Against

hidden variables but to an indeterminism in nature itself.[24] Eddington proclaimed "It is a consequence of the advent of the quantum theory that physics is no longer pledged to a scheme of deterministic law".[25]

Popular and philosophical writings

Eddington wrote a parody of

The Rubaiyat of Omar Khayyam, recounting his 1919 solar eclipse experiment. It contained the following quatrain:[26]

Oh leave the Wise our measures to collate
           One thing at least is certain, LIGHT has WEIGHT,
One thing is certain, and the rest debate—
Light-rays, when near the Sun, DO NOT GO STRAIGHT.

During the 1920s and 30s, Eddington gave numerous lectures, interviews, and radio broadcasts on relativity, in addition to his textbook

The Mathematical Theory of Relativity
, and later, quantum mechanics. Many of these were gathered into books, including The Nature of the Physical World and New Pathways in Science. His use of literary allusions and humour helped make these difficult subjects more accessible.

Eddington's books and lectures were immensely popular with the public, not only because of his clear exposition, but also for his willingness to discuss the philosophical and religious implications of the new physics. He argued for a deeply rooted philosophical harmony between scientific investigation and religious mysticism, and also that the positivist nature of relativity and quantum physics provided new room for personal religious experience and free will. Unlike many other spiritual scientists, he rejected the idea that science could provide proof of religious propositions.

His popular writings made him a household name in Great Britain between the world wars.

Death

Eddington died of cancer in the Evelyn Nursing Home, Cambridge, on 22 November 1944.[27] He was unmarried. His body was cremated at Cambridge Crematorium (Cambridgeshire) on 27 November 1944; the cremated remains were buried in the grave of his mother in the Ascension Parish Burial Ground in Cambridge.

Cambridge University's North West Cambridge development has been named Eddington in his honour.

Eddington was played by David Tennant in the television film Einstein and Eddington, with Einstein played by Andy Serkis. The film was notable for its groundbreaking portrayal of Eddington as a somewhat repressed gay man. It was first broadcast in 2008.

The actor Paul Eddington was a relative, mentioning in his autobiography (in light of his own weakness in mathematics) "what I then felt to be the misfortune" of being related to "one of the foremost physicists in the world".[28]

Obituaries

  • Obituary 1 by
    Astrophysical Journal
    101 (1943–46) 133
  • Obituary 2 by
    A. Vibert Douglas, Journal of the Royal Astronomical Society of Canada
    , 39 (1943–46) 1
  • Obituary 3 by Harold Spencer Jones and E. T. Whittaker, Monthly Notices of the Royal Astronomical Society 105 (1943–46) 68
  • Obituary 4 by Herbert Dingle, The Observatory 66 (1943–46) 1
  • The Times, Thursday, 23 November 1944; pg. 7; Issue 49998; col D: Obituary (unsigned) – Image of cutting available at O'Connor, John J.; Robertson, Edmund F., "Arthur Eddington", MacTutor History of Mathematics Archive, University of St Andrews

Honours

Awards and honors

Named after him

Service

In popular culture

Publications

See also

Astronomy

Science

People

  • List of science and religion scholars

Other

References

  1. ^ Arthur Eddington at the Mathematics Genealogy Project
  2. S2CID 121473352
    .
  3. ^
    JSTOR 6491
  4. ^
    doi:10.1093/mnras/77.1.16
    .
  5. ISBN 090219884X. Archived from the original
    (PDF) on 24 January 2013. Retrieved 1 April 2016.
  6. ^ a b c d e f Douglas, A. Vibert (1956). The Life of Arthur Eddington. Thomas Nelson and Sons. pp. 92–95.
  7. ^ "Library and Archive Catalogue". Royal Society. Retrieved 29 December 2010.
  8. doi:10.1038/435020a
    .
  9. ^
    ISBN 978-0521257466
    .
  10. ^
    doi:10.1098/rsta.1920.0009
    .
  11. S2CID 145254889
    .
  12. S2CID 119203172
    .
  13. doi:10.1063/1.3099578
    .
  14. ^ As related by Eddington to Chandrasekhar and quoted in Walter Isaacson "Einstein: His Life and Universe", p. 262
  15. ISBN 978-3642453021
    .
  16. S2CID 125122360
    .
  17. ISBN 978-0316089081
    .
  18. ^ "2018 CODATA Value: inverse fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
  19. ISBN 978-0198519492
    .
  20. ^
    doi:10.1088/2058-7058/18/10/30
    . Retrieved 17 September 2022.
  21. ^ "Eddington number". 16 March 2008.
  22. doi:10.1088/2058-7058/25/07/24
    .
  23. ^ De Konick, Charles (2016). The Writings of Charles De Koninck Volume 1. University of Notre Dame Press.
  24. ^
    OCLC 615199716
    .
  25. ^ Bell, Ian F.A. (2023). Critic as Scientist The Modernist Poetics of Ezra Pound. Taylor & Francis. p. 1898.
  26. ^ Douglas, A. Vibert (1956). The Life of Arthur Eddington. Thomas Nelson and Sons. p. 44.
  27. ISBN 978-1541762251
    .
  28. ^ Quakers and the Arts: "Plain and Fancy"- An Anglo-American Perspective, David Sox, Sessions Book Trust, 2000, p. 65
  29. ^ "Arthur Stanley Eddington". American Academy of Arts & Sciences. 9 February 2023. Retrieved 5 July 2023.
  30. ^ "Past Winners of the Catherine Wolfe Bruce Gold Medal". Astronomical Society of the Pacific. Archived from the original on 21 July 2011. Retrieved 19 February 2011.
  31. ^ "Henry Draper Medal". National Academy of Sciences. Archived from the original on 26 January 2013. Retrieved 19 February 2011.
  32. ^ "Arthur Eddington". www.nasonline.org. Retrieved 5 July 2023.
  33. ^ "A.S. Eddington (1882–1944)". Royal Netherlands Academy of Arts and Sciences. Retrieved 25 January 2016.
  34. ^ "APS Member History". search.amphilsoc.org. Retrieved 5 July 2023.
  35. ^ "Generalforsamling – Norsk Astronomisk Selskap".
  36. ^ a b c d Who's who entry for A.S. Eddington.
  37. ^ "Sir Arthur Eddington | Apr. 16, 1934". Time.
  38. ^ "Structural Realism": entry by James Ladyman in the Stanford Encyclopedia of Philosophy

Further reading

External links
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